Sort of follow on from my previous question.
Shields take an action to don or doff.
In the previous question it was discussed that the reason for this might be needing to strap the shield to your arm/unstrap it.
If your other arm is occupied (caught in a trap, or temporarily turned evil), can you don or doff a shield with just one arm free?
The reason I think you might not be able to is the difficulty of handling the straps with the hand going into the shield.
The rules don't specify; it's up to the DM
As you've noted in your question, the rules specify the time required to don or doff a piece of armor or a shield. However, the rules don't state anything else about what's needed to don or doff armor or shields - specifically, they don't specify whether donning or doffing armor or a shield requires one or both hands to do.
As such, it's up to the DM to decide whether a shield can be donned or doffed with just one hand. For armor, it seems likely that the DM would rule that both hands are needed to put it on or take it off. Shields are a bit more of a gray area, so the DM would ultimately need to make a decision on the matter for themselves.